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arXiv · 1805.03996

On approximate Connes-biprojectivity of dual Banach algebras

S. F. Shariati·A. Pourabbas·A. Sahami
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Abstract

In this paper, we introduce a notion of approximate Connes-biprojectivity for dual Banach algebras. We study the relation between approximate Connes-biprojectivity, Johnson pseudo-Connes amenability and $φ$-Connes amenability. We propose a criterion to show that some certain dual triangular Banach algebras are not approximately Connes-biprojective. Next we show that for a locally compact group $G$, the Banach algebra $M(G)$ is approximately Connes-biprojective if and only if $G$ is amenable. Finally for an infinite commutative compact group $G$ we show that the Banach algebra $L^2(G)$ with convolution product is approximately Connes-biprojective, but it is not Connes-biprojective.

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BibTeXRIS

S. F. Shariati, A. Pourabbas, A. Sahami. 2018-11-17. On approximate Connes-biprojectivity of dual Banach algebras. https://arxiv.org/abs/1805.03996

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